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Simplifying 8x2 + 9 = 55x Reorder the terms: 9 + 8x2 = 55x Solving 9 + 8x2 = 55x Solving for variable 'x'. Reorder the terms: 9 + -55x + 8x2 = 55x + -55x Combine like terms: 55x + -55x = 0 9 + -55x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -6.875x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -6.875x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -6.875x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -6.875x + x2 = 0 + -1.125 -6.875x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -6.875x + x2 = -1.125 The x term is -6.875x. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875x + 11.81640625 + x2 = -1.125 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = -1.125 + 11.81640625 Combine like terms: -1.125 + 11.81640625 = 10.69140625 11.81640625 + -6.875x + x2 = 10.69140625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 10.69140625 Calculate the square root of the right side: 3.26977159 Break this problem into two subproblems by setting (x + -3.4375) equal to 3.26977159 and -3.26977159.Subproblem 1
x + -3.4375 = 3.26977159 Simplifying x + -3.4375 = 3.26977159 Reorder the terms: -3.4375 + x = 3.26977159 Solving -3.4375 + x = 3.26977159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = 3.26977159 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 3.26977159 + 3.4375 x = 3.26977159 + 3.4375 Combine like terms: 3.26977159 + 3.4375 = 6.70727159 x = 6.70727159 Simplifying x = 6.70727159Subproblem 2
x + -3.4375 = -3.26977159 Simplifying x + -3.4375 = -3.26977159 Reorder the terms: -3.4375 + x = -3.26977159 Solving -3.4375 + x = -3.26977159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = -3.26977159 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -3.26977159 + 3.4375 x = -3.26977159 + 3.4375 Combine like terms: -3.26977159 + 3.4375 = 0.16772841 x = 0.16772841 Simplifying x = 0.16772841Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.70727159, 0.16772841}
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